These advantages have motivated an increasing number of researchers in recent
years to develop spherical microphone array systems, to study spherical array
configurations, to develop algorithms for spherical arrays, and to apply these arrays
in a wide range of applications. This growing activity has provided the author with
the motivation and inspiration to write this book, with the aim of presenting the
fundamentals of spherical array processing in a tutorial manner suitable for
researchers, graduate students, and engineers interested in this topic.
The first two chapters provide the reader with the necessary mathematical and
physical background, including an introduction to the spherical Fourier transform
and to the formulation of plane-wave sound fields in the spherical harmonics
domain. The third chapter covers the theory of spatial sampling, which becomes
useful when selecting the positions of microphones to sample sound pressure
functions in space. The next chapter presents various spherical array configurations,
including the popular configuration based on a rigid sphere. The fifth chapter
introduces the concept of beamforming and its basic equations, including popular
design methods such as delay-and-sum and regular beamforming. The following
chapter presents methods for the optimal design of beam patterns, formulated to
achieve various objectives such as maximum robustness, maximum directivity, or
minimum side-lobe level. The final chapter develops more advanced array processing algorithms such as the minimum variance distortionless response (MVDR) algorithm. These algorithms aim to enhance a desired signal while attenuating undesired noise components in the sound field by exploring their unique formulation in the spherical harmonics domain.